The present invention pertains to the field of nonlinear optics and in particular to second harmonic generation.
An article entitled "Nonlinear Optical Properties of Solids: Energy Considerations", Physical Review, Vol. 130, No. 3, May 1, 1963, pp. 919-929, by P. S. Pershan discusses second harmonic generation by means of electric quadrupole effects. In particular his analysis determines that for an isotropic material a plane wave cannot provide collinear second harmonic generation. He determined that in order to produce the second harmonic radiation in an isotropic material it is necessary to utilize two noncollinear plane waves at the fundamental frequency.
An article entitled "Optical Quadrupole Sum-Frequency Generation in Sodium Vapor", Physical Review Letters, Vol. 37, No. 7, Aug. 16, 1976, pp. 431-434, by D. S. Bethune, R. W. Smith, and Y. R. Shen and an article entitled "Sum-Frequency Generation Via a Resonant Quadrupole Transition in Sodium", Physical Review A, Vol. 17, No. 1, January 1978, pp. 277-292, by D. S. Bethune, R. W. Smith, and Y. R. Shen both indicate that collinear quadrupole sum-frequency generation is not possible in an isotropic medium. These articles then go on to disclose sum frequency generation by means of three-wave mixing which entails the use of two noncollinear electromagnetic waves.
An article entitled "Optical Difference-Frequency Generation in Atomic Thallium Vapor", Physical Review Letters, Vol. 38, No. 2, Jan. 10, 1977, pp. 59-62, by A. Flusberg, T. Mossberg, and S. R. Hartmann discloses sum frequency generation by means of two collinear laser beams in the presence of a weak static transverse magnetic field. The article indicates that the transverse magnetic field breaks the symmetry of the medium, which symmetry breaking allows three-wave mixing to occur by an E2 interaction.
An article entitled "Optical Second-Harmonic Generation in Gases: "Rotation" of Quadrupole Moment in Magnetic Field", Physical Review Letters, Vol. 38, No. 16, Apr. 18, 1977, pp. 894-898, by M. Matsuoka, H. Nakatsuka, H. Uchiki, and M. Mitsunaga discusses the fact that whereas collinear second harmonic generation was not possible in sodium, it was possible to provide a collinear three-wave mixing in the medium with transverse magnetization. The article then reports an experiment in which a second harmonic was generated from sodium and calcium vapor in a transverse dc magnetic field.
An article entitled "Optical Second-Harmonic Generation in Atomic Thallium Vapor", Optics Communications, Vol. 25, No. 1, April 1978, pp. 121-124, by T. Mossberg, A. Flusberg, and S. R. Hartmann discloses second harmonic generation in atomic thallium vapor when the fundamental was tuned to half the resonance frequency in the following transitions: 6.sup.2 P.sbsb.1/2-7.sup.2 P.sbsb.1/2 and 6.sup.2 P.sbsb.1/2-8.sup.2 P.sbsb.1/2 in the absence of any external field. The article reports that "SHG on these transitions is very surprising, especially in view of the lack of an appreciable multipole moment on either transition". The article explains their result in terms of a partial photoionization of the 7.sup.2 P.sbsb.1/2 state population. This gives rise to a radial electric field due to the macroscopic charge separation, which radial field breaks the symmetry and induces the second harmonic generation.
An article entitled "Spontaneous-Field-Induced Optical Second-Harmonic Generation in Atomic Vapors", Physical Review Letters, Vol. 43, No. 16, Oct. 15, 1979, pp. 1154-1157, by K. Miyazaki, T. Sato, and H. Kashiwagi discusses second harmonic generation in centrosymmetric media. They discuss the fact that SHG in centrosymmetric media is strictly forbidden by parity conservation or symmetry. In the paper they discuss a theory and an experiment to show that a laser pulse with a spatial intensity gradient irradiating a dispersive atomic vapor induces a static electric field and generates second harmonic in the atomic medium due to the E1 interaction. They point out that the presence of any external field applied to the medium or any resonant condition is not necessary. The basis upon which their prediction is based is the fact that a static electric field may be induced in the medium by means of the application of the aforementioned laser pulse. This assumption is erroneous. A study of the second harmonic signal versus laser intensity in FIG. 3 of the Miyazaki et al article indicates that the intense laser beam applied by the authors has produced an electric field by means of multistep photoionization and not by means of the production of a static electric field.